Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Sat, 11 Jan 2025 01:13:35 -0800 Organization: A noiseless patient Spider Lines: 32 Message-ID: References: <59af1502-0bc9-4266-b556-6164edb6a8d4@att.net> <9a22a29bfd5af29db5bad5f3cae537665b8dafd7@i2pn2.org> <81834850e9e4fdedeb38ddc1da4df4a1ebe34e07@i2pn2.org> <2f29dfa35175206d66b46a7e27ca16fe6ae1a1eb@i2pn2.org> <09d0c621cf583928d69f8837bad7a2bd66461829@i2pn2.org> <725291dea848b0d681f7d983a026a5464fec86c9@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 11 Jan 2025 10:13:37 +0100 (CET) Injection-Info: dont-email.me; posting-host="ce024765705e8ff52c0316de8f77e49c"; logging-data="566046"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+jMipa4qbePxRBZXRxE7fOm4pOg0iZ0pY=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:Ra5/5t8VZ9KPgAncj1w7S2+eVHU= Content-Language: en-US In-Reply-To: Bytes: 3370 On 1/11/2025 1:12 AM, Chris M. Thomasson wrote: > On 1/11/2025 12:55 AM, WM wrote: >> On 10.01.2025 22:58, joes wrote: >>> Am Fri, 10 Jan 2025 22:30:52 +0100 schrieb WM: >>>> On 10.01.2025 21:03, joes wrote: >>>>> Am Fri, 10 Jan 2025 20:22:44 +0100 schrieb WM: >>>> >>>>>> If actual infinity is invariable, then we can take the set ℕ and >>>>>> consider it as invariable. When we add further elements, it grows. >>>>> The set N u {w}, for example, is not equal to N. You can't call that >>>>> invariable. >>>> Every set in ZF is invariable. >>> Right. N stays N even when you construct a new set N u {k} (which is >>> a different set only if k !e N}. So N doesn't "grow". >> >> That contradicts the possibility of bijections, because if it has been >> finished, you can add further elements and violate completeness. But >> since you cannot comprehend this, look at the simpler theorem: >> >> Every union of FISONs which stay below a certain threshold stays below >> that threshold. >> >> I never met a student who doubted this. And I am sure I will never >> meet a contrary opinion in a sober brain. > > > wow. You make we want to do drugs right now! Smoke shrooms and drink > weed? wow. You are a very special person! https://youtu.be/7YvAYIJSSZY?list=RD7YvAYIJSSZY ROFL!!!!!!!!!!!